In the article:
Human mobility and time spent at destination: Impact on spatial epidemic spreading.
C Poletto, M Tizzoni and V Colizza
Journal of Theoretical Biology, 338:41-58 (2013) doi: 10.1016/j.jtbi.2013.08.032.
we present a detailed analysis of the interesting features that appear when a non-Markovian mobility is considered in a spatially structured epidemic model. We use the theoretical framework, already introduced in our previous work (Scientific Reports 2,476 2012), that takes into account the heterogeneous distribution of the length of stay of travelers and we compute the global epidemic threshold at the metapopulation level. Additionally, our framework allows us to study the effect of changes in the traveling behavior in response to the infection, by considering a scenario in which sick individuals do not leave their home location. Finally, we compare the results of our non-Markovian framework with those obtained with a classic Markovian approach and find relevant differences between the two, in the estimate of the epidemic invasion potential, as well as of the timing and the pattern of its spatial spread. These results highlight the importance of properly accounting for host trip duration in epidemic models and open the path to the inclusion of such an additional layer of complexity to the existing modeling approaches.